01 - In a medium bowl, whisk together the salsa verde, olive oil, ground cumin, garlic powder, smoked paprika, kosher salt, and black pepper until well combined.
02 - Place the chicken breasts in a large resealable plastic bag or shallow dish. Pour half of the salsa verde mixture over the chicken, reserving the remaining half for grilling. Seal and refrigerate for at least 30 minutes, or up to 4 hours for deeper flavor penetration.
03 - Preheat the grill to medium-high heat (approximately 375°F to 400°F). Lightly oil the grill grates to prevent the chicken from sticking.
04 - Remove the chicken from the marinade and discard the used marinade. Place the chicken breasts on the grill, cover, and cook for 5 to 7 minutes per side until the internal temperature reaches 165°F and juices run clear.
05 - During the last 2 minutes of grilling, spoon the reserved salsa verde mixture over each chicken breast and distribute the shredded Pepper Jack cheese evenly on top. Close the grill lid and allow the cheese to melt completely.
06 - Transfer the chicken to a serving platter, garnish with chopped fresh cilantro, and serve immediately with lime wedges alongside.